Sadie and her children went into a grocery store where they sell peaches for $1.25 each and mangos for $0.50 each. Sadie has $9.50 to spend and must buy no less than 13 peaches and mangos altogether. If Sadie decided to buy 4 mangos, determine all possible values for the number of peaches that she could buy. Answer:

Question

Sadie and her children went into a grocery store where they sell peaches for  $1.25 each and mangos for  $0.50 each. Sadie has  $9.50 to spend and must buy no less than 13 peaches and mangos altogether. If Sadie decided to buy 4 mangos, determine all possible values for the number of peaches that she could buy. Answer:

Bytelearn · Accepted Answer

Calculate Cost of Mangos: Calculate the total cost of 4 mangos. Since each mango costs $0.50, we multiply the number of mangos by the cost per mango. 4 mangos * $0.50/mango = $2.00Subtract Mango Cost: Subtract the cost of the mangos from the total amount Sadie has to spend. Sadie has $9.50 to spend, and she has already spent $2.00 on mangos. $9.50 - $2.00 = $7.50 This is the amount remaining for purchasing peaches.Calculate Maximum Peaches: Calculate the maximum number of peaches Sadie can buy with the remaining money. Since each peach costs $1.25, we divide the remaining amount by the cost per peach. $7.50 / $1.25/peach = 6 peachesCheck Total Fruits: Check if the total number of fruits meets the minimum requirement. Sadie has bought 4 mangos and can buy up to 6 peaches. 4 mangos + 6 peaches = 10 fruits This does not meet the requirement of buying at least 13 fruits.Determine Peaches Needed: Determine the number of peaches Sadie can buy to meet the minimum fruit requirement. Sadie needs to buy at least 13 - 4 = 9 peaches to meet the minimum requirement of 13 fruits.Check Affordability: Check if Sadie has enough money to buy 9 peaches. 9 peaches * $1.25/peach = $11.25 Sadie only has $7.50 left to spend on peaches, so she cannot buy 9 peaches.Find Maximum Peaches: Find the greatest number of peaches Sadie can buy with the remaining money that also meets the minimum fruit requirement. Sadie can buy 6 peaches with her remaining $7.50, but this does not meet the minimum requirement of 13 fruits. Therefore, she must buy fewer mangos or find a different solution.Re-evaluate Constraints: Since the previous steps led to a contradiction, we need to re-evaluate our calculations and constraints. We need to find a number of peaches that Sadie can afford with $7.50 that, when added to the 4 mangos, equals or exceeds 13 fruits in total. Let's denote the number of peaches as P. P + 4 mangos ≥ 13 fruits P ≥ 13 - 4 P ≥ 9Adjust Mango Quantity: Calculate the cost for 9 peaches. 9 peaches * $1.25/peach = $11.25 This exceeds Sadie's remaining budget of $7.50, so she cannot buy 9 peaches.Calculate Peaches Affordability: Adjust the number of peaches to fit the budget. Since Sadie cannot afford 9 peaches, let's try with 8 peaches. 8 peaches * $1.25/peach = $10.00 This still exceeds Sadie's remaining budget of $7.50.Check Fruit Requirement: Continue adjusting the number of peaches. Try with 7 peaches. 7 peaches * $1.25/peach = $8.75 This still exceeds Sadie's remaining budget of $7.50.Adjust Mango Quantity: Continue adjusting the number of peaches. Try with 6 peaches. 6 peaches * $1.25/peach = $7.50 This fits Sadie's remaining budget exactly, and when added to the 4 mangos, gives a total of 10 fruits.Calculate Peaches Affordability: Since Sadie needs at least 13 fruits, and 6 peaches and 4 mangos only make 10 fruits, she cannot buy 6 peaches. She needs to buy at least 9 fruits to meet the minimum requirement when combined with the 4 mangos. Since Sadie cannot afford 9 peaches, she cannot meet both the budget constraint and the minimum fruit requirement if she buys 4 mangos.Check Fruit Requirement: Re-evaluate the constraints and find a solution that meets both the budget and the minimum fruit requirement. Since Sadie cannot meet the minimum fruit requirement by buying 4 mangos and the maximum number of peaches she can afford, she needs to buy fewer mangos to be able to buy more peaches.Adjust Mango Quantity: Determine the new number of mangos Sadie can buy to afford more peaches. If Sadie buys 3 mangos instead of 4, she will spend: 3 mangos * $0.50/mango = $1.50 This leaves her with: $9.50 - $1.50 = $8.00 for peaches.Calculate Peaches Affordability: Calculate the number of peaches Sadie can buy with $8.00. $8.00 / $1.25/peach = 6.4 peaches Since Sadie cannot buy a fraction of a peach, she can buy up to 6 peaches with $8.00.Check Fruit Requirement: Check if the new combination of 3 mangos and 6 peaches meets the minimum fruit requirement. 3 mangos + 6 peaches = 9 fruits This still does not meet the minimum requirement of 13 fruits.Adjust Mango Quantity: Since buying 3 mangos still does not allow Sadie to meet the minimum fruit requirement, she needs to buy even fewer mangos. If Sadie buys 2 mangos, she will spend: 2 mangos * $0.50/mango = $1.00 This leaves her with: $9.50 - $1.00 = $8.50 for peaches.Calculate Peaches Affordability: Calculate the number of peaches Sadie can buy with $8.50. $8.50 / $1.25/peach = 6.8 peaches Since Sadie cannot buy a fraction of a peach, she can buy up to 6 peaches with $8.50.Check Fruit Requirement: Check if the new combination of 2 mangos and 6 peaches meets the minimum fruit requirement. 2 mangos + 6 peaches = 8 fruits This still does not meet the minimum requirement of 13 fruits.Adjust Mango Quantity: Since buying 2 mangos still does not allow Sadie to meet the minimum fruit requirement, she needs to buy even fewer mangos. If Sadie buys 1 mango, she will spend: 1 mango * $0.50/mango = $0.50 This leaves her with: $9.50 - $0.50 = $9.00 for peaches.Calculate Peaches Affordability: Calculate the number of peaches Sadie can buy with $9.00. $9.00 / $1.25/peach = 7.2 peaches Since Sadie cannot buy a fraction of a peach, she can buy up to 7 peaches with $9.00.Check Fruit Requirement: Check if the new combination of 1 mango and 7 peaches meets the minimum fruit requirement. 1 mango + 7 peaches = 8 fruits This still does not meet the minimum requirement of 13 fruits.No Solution: Since buying 1 mango still does not allow Sadie to meet the minimum fruit requirement, she needs to buy no mangos and all peaches. With $9.50 to spend on peaches alone: $9.50 / $1.25/peach = 7.6 peaches Sadie can buy up to 7 peaches with $9.50.Check if buying 7 peaches meets the minimum fruit requirement. 7 peaches = 7 fruits This does not meet the minimum requirement of 13 fruits.Since Sadie cannot meet the minimum requirement of 13 fruits with her budget, there is no solution to the problem as stated. Sadie cannot buy 4 mangos and at least 13 fruits in total with $9.50.

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